If I use a AWD number to get a better deal with Avis, would I have to prove where I found it?
When using an Avis discount code, either online or over the phone, when making a reservation. You generally will not have to prove WHERE you found it. (Unless it is an AWD number to get a better deal with Avis that is included on a paper coupon... in which case you'd have to bring the coupon with you to the checkout).
What you may be asked at the rental counter, is to show proof of eligibility for the Avis discount code. If it is associated with a professional association (example -- Society of Professional Engineers) or a membership program (example -- Delta Skymiles) and you are asked, you would be required to show proof of membership in order to recieve the discount associated with the AWD number. This would probably mean you would show your membership card, or request written proof of membership from the organization before you rent the car.
If the Avis discount code is associated with a corporate account, if asked, you would be required to provide proof of employment with that company, either with employee ID or a current paystub that contains the same address as that on your drivers license.
You may not be asked to provide proof of eligibility for discount at the counter, but it's best to be prepared to be able to do so.